Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #393×C71 | C2 |
| hypercenter | #393 | D71 |
| hypocenter | C71 | #2398 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic71 | C2 | semidirect |
| 3. #17985941 | C2 | semidirect |
| 4. #17985926 | C2 | semidirect |
| 5. #17985924 | C2 | semidirect |
| 7. #17985910 | C2 | semidirect |
| 8. C22⋊C4×Dic71 | C2 | semidirect |
| 9. #17985846 | C2 | semidirect |
| 10. #17985844 | C2 | semidirect |
| 11. #393×C71 | C2 | semidirect |
| 139. C71 | #2398 | semidirect |
| 147. #393 | D71 | semidirect |